Complex convexity and vector-valued Littlewood–Paley inequalities
نویسندگان
چکیده
Let 2 ≤ p < ∞ and let X be a complex Banach space. It is shown that X is p-uniformly PL-convex if and only if there exists λ > 0 such that ‖f‖Hp(X) ≥ ( ‖f(0)‖p + λ ∫ D (1− |z|2)p−1‖f ′(z)‖pdA(z) )1/p , for all f ∈ Hp(X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided. AMS Subject Class. 46B20,46L52
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